The road to useful quantum computing

Every day, you’ve got critical forecasting and optimization problems to solve. Whether the problem at hand involves anomaly detection, hedging, portfolio optimization, pricing, risk analysis, or trading strategy, time is of the essence. Unfortunately, there’s too much data, too many variables, and other factors demanding extreme computing power. The stakes are high, but even with a supercomputer, approximations have to suffice; accuracy and reliability have to suffer. You’ve heard that quantum computers may someday come to the rescue and offer a competitive advantage in some cases, but you’ve also heard that this day is still in the future. However, recent advancements toward so-called “logical qubits” indicate that the time to start paying attention to this technology is now.

Depending on who you ask, the duration of our journey into quantum computing thus far can be measured in decades. Richard Feynman suggested that quantum mechanics might be leveraged for computation in 1959 [1], Paul Benioff described the first model of a quantum computer in 1980 [2], and the first quantum computer was built in 1998 [1]. Some will go back more than a century, however, to the discovery of quantum mechanics in 1900 [3].

For comparison with digital computing, mechanical calculators date back to the 17th century. Automation was introduced in the 1830s, the electronic Z3 was built in 1941, the general-purpose ENIAC was built in 1946, and the transistor was invented in 1948 [4].

The road has been a long one, and considerable progress has been made. In 1998, we had two qubits in a laboratory that couldn’t maintain quantum information long enough to be useful. In 2024, we have 256 qubits accessible via the cloud that can maintain quantum information long enough to demonstrate computation. And in laboratories, we have three quantum computers boasting more than 1,000 qubits each. Qubits are the fundamental units of quantum information, and their quantity is one measure of a quantum computer’s capabilities.

In terms of usefulness, there are three classifications of how useful a quantum computer can be. Utility, advantage, and supremacy.

Utility vs advantage vs supremacy

The first of these terms to be used was “quantum supremacy.” It is characterized by a quantum computer solving a problem that is infeasible for classical computers, such as complex derivatives pricing, large portfolio optimization, and the optimal execution of large trades. With our current knowledge, we don’t have the processing power or memory available to solve these types of problems with classical computers within reasonable timeframes.

Next came “quantum advantage.” The threshold does not require that the problem be otherwise unsolvable, however the initial usage did suggest a speed advantage over classical computation. It has evolved to suggest other advantages, such as cost, space, and energy efficiency. Importantly, it suggests that the problem is of commercial interest, such as financial risk management problems.

More recently, the term “quantum utility” has been introduced. While it doesn’t suggest advantages over classical computation, it does suggest graduation from “toy problems” and proof-of-concept demonstrations. Error rates need to be low enough and qubit counts high enough to perform commercially useful computation, even though classical computation remains a viable option.

“Advantage” and “utility” require fault-tolerant quantum computing.

road to useful quantum computing

The two eras of quantum computing

As coined by Caltech Professor Dr. John Preskill, we are currently in the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. This is the road before the highway, and it is characterized by the terms “noise” and “intermediate-scale.”

Quantum information is extremely sensitive to the surrounding environment, and this “noise,” which can arise from many sources, causes errors during computation. The qubit counts are enough for proof-of-concept demonstrations but are not at a large enough scale for real-world applicability. Current qubits also have short lifetimes, which means that they can’t preserve quantum information long enough to complete the types of computation we want to perform.

Our goal is to transition into the Fault-Tolerant Quantum Computing (FTQC) era, which will be the highway of quantum computing. Errors will be corrected, greatly improving the accuracy of computation. Qubit counts will be higher, supporting larger algorithms. And qubit lifetimes will be longer, allowing computation to complete. While you may find the term FTQC further broken down into sub-eras with different qubit counts and different error rates, the underlying theme is useful quantum computation. That’s what we’re building them for.

Because we are not yet in the FTQC era, claims of utility and advantage must be met with skepticism. Claims of supremacy have different rules.

Shortfalls of “supremacy” experiments

Over the past few years, several claims of “supremacy” have been made. One of the shortcomings of this term, however, becomes quickly apparent each time. Although these experiments demonstrate that supremacy is possible, the selected problems are not immediately of commercial interest. And while such interest may someday be found, it is not a requirement of the term that the problem has any actual usefulness.

Another problem is that classical computation has already begun to challenge these conclusions. At the time of the experiments, “supremacy” was indeed demonstrated. But novel classical approaches, inspired by the “supremacy” experiments, have essentially negated them afterward. The most famous example is the very first one, a 200-second quantum experiment for which Google claimed classical algorithms would need 10,000 years and IBM’s rebuttal needs a mere 2.5 days [5]. Another challenge comes from tensor networks [6], which can efficiently solve problems meant for near-term quantum computers. Therefore, it is important that these “supremacy” claims withstand scrutiny for some time to ensure that they hold up over the long term [7].

"We would like quantum supremacy not only to have been achieved but to stay achieved.”

– Scott Aaronson [8]

Yet another problem is that verification can be computationally expensive. This doesn’t apply to all problems, as integer factorization is very hard to do but very simple to verify. But other problems can be as hard to verify as they are to solve. While a quantum computer may be able to “solve” a problem that a supercomputer can’t, it may not be possible in all cases to verify that the quantum computer solved the problem [9].

Most importantly, the term does not require an error-free solution. These experiments are demonstrations of speed, with no minimum standards regarding accuracy. In the real world, however, accurate solutions are important. Claims of utility and advantage are going to require accurate solutions, and accurate solutions are going to require error correction [10]. Error correction introduces the concept of logical qubits.

Logical qubits & error correction

Logical qubits are the onramps to the FTQC highway. Analogous to how many local roads can feed into a single onramp, many physical qubits are encoded into a single logical qubit.

We currently encode quantum information onto physical qubits, which experience high error rates. These physical qubits might be individual atoms or ions, they might be special electronic circuitry, or they are one of the other “modalities” in development. Whichever we choose, we will stay in the NISQ era.

That is unless we apply quantum error correction (QEC). There are countless quantum error correction codes (QECC) being researched that would arrange physical qubits into logical qubits. The quantum information for a logical qubit is distributed over many of its physical qubits, known as data qubits. Auxiliary qubits, known as syndrome qubits, are used to detect errors on neighboring data qubits, and then corrections are made, as needed, to the data qubits. This preserves the quantum information of the logical qubit, allows longer computation, and results in a lower error rate for the logical qubit than for its component physical qubits.

Logical qubits exist. Quantities need to go up, error rates need to come down, and lifetimes need to get longer, but they do already exist.

road to useful quantum computing

The road travelled in 2023

Progress was made throughout the year, both theoretically and experimentally. While these advancements have not put us on the FTQC highway, they have closed the distance to the onramps. In chronological order, the top developments include:

On February 22, Google published results showing that a logical qubit with more physical qubits had a lower error rate, as theorized, than a logical qubit with fewer physical qubits [11].
On March 21, Yale published results showing that quantum error correction, as theorized, extends the lifetime of quantum information [12].
On March 24, the Chinese Academy of Sciences, Tsinghua University, and Fuzhou University published results showing an extension of quantum information lifetime [13].
On March 28, PsiQuantum proposed a method that doesn’t lower error rates, but improves the tolerance for errors, raising the threshold under which fault tolerance becomes possible [14].
On April 12, Cornell and Google published results showing progress toward topological quantum computing, a theoretical approach to protecting quantum information [15].
On May 9, Quantinuum, Harvard, and Caltech published results showing progress toward topological quantum computing [16].
On May 25, the University of Chicago published a method to detect noise and adjust for it in real-time, minimizing the errors affecting the quantum information [17].
On June 6, QC Design introduced Plaquette, an open-source software package for studying quantum error correction and fault tolerance [18].
On July 13, Quantinuum announced that it used logical qubits to calculate the ground state energy of a hydrogen molecule [19].
On August 15, IBM published an error correction code with an error threshold comparable to existing codes, but requiring far fewer physical qubits [20].
On August 16, QuEra and four universities published a code that scales better than existing codes, requiring hundreds or even thousands fewer physical qubits even at small scales [21].
On September 11, Riverlane and the University of Sheffield published a fast, resource-efficient classical decoder capable of detecting errors without causing computation bottlenecks [22].
On September 19, Quantinuum, QuTech, and the University of Stuttgart published the results of using logical qubits to perform a small basic arithmetic problem [23].
On October 12, Harvard, MIT, and QuEra published the largest demonstration of multi-qubit operations with an error rate below the required threshold for fault tolerance [24].
On November 1, ETH Zurich announced participation in two projects involving connections between two logical qubits [25].
On November 21, USTC and two other universities published results supporting an approach to making quantum computers more resilient to noise [26].
On November 27, AWS announced progress toward suppressing one type of error, theoretically making overall error correction more efficient [27].
On December 6, Harvard, QuEra, and others published results setting new records in logical qubit count and logical qubit size, while demonstrating lower logical error rates [28].
On December 19, Alice & Bob announced the tape out of a prototype chip designed specifically to demonstrate logical qubits [29].

Already in 2024, QuEra has announced a roadmap to 100 logical qubits using 10,000+ physical qubits by 2026 [30]. Alice & Bob then teased 100 logical qubits using 1,500 physical qubits [31], although the timeframe isn’t public yet. Neither has published target error rates or qubit lifetimes, but both roadmaps look to provide onramps to the FTQC highway. Most recently, Infleqtion announced a roadmap to >100 logical qubits using 40,000 physical qubits by 2028, and it includes some performance targets [32].

Error suppression and mitigation in 2023

While waiting to transition into the FTQC era, research is ongoing in three other areas. Error suppression reduces the occurrence of errors so that there are fewer to detect and correct with error correction codes. Error mitigation analyzes the errors that a quantum computer makes, and then adjusts the results of the computation using classical algorithms. Furthermore, we are trying to find and develop better qubits, however those initiatives are both too numerous and too secretive to list.

On April 4, Q-CTRL shared results demonstrating error suppression and mitigation on an algorithm that is used to solve optimization problems [33].
On September 10, Infleqtion published an introduction to software that suppresses and mitigates errors [34].
On September 29, IBM published the results of error mitigation on an algorithm used for quantum chemistry and other problems [35].
On November 28, Q-CTRL announced error suppression as an embedded, no-additional-cost option for IBM’s Pay-As-You-Go plans [36].

While suppression and mitigation are not enough by themselves to establish fault tolerance, they can noticeably improve the quality of the results from NISQ quantum computers. They can help demonstrate, on a small scale, that these computers work.

Different architectures and plausibility

While many architectures are actively in development, and more still are being researched, the progress made in 2023 hints at the early frontrunners. QuEra, Infleqtion, and Alice & Bob have the only three roadmaps with logical qubits, also Quantinuum is executing algorithms with logical qubits.

QuEra and partners are using physical qubits that are individual neutral atoms. QuEra also holds the distinction of having the largest publicly-available quantum computer.
Infleqtion is also using neutral atoms as physical qubits, however they will be using two species of atoms instead of one. Infleqtion claims the largest demonstrated quantum computer.
Alice & Bob is using a fabricated “cat qubit,” which is designed to suppress one type of error at the expense of another type of error but simplify error correction overall.
Quantinuum and partners are using physical qubits that are ionized atoms. Quantinuum holds the record for a qualitative measure of qubits, called Quantum Volume (QV).

Each of these modalities has its strengths and weaknesses, not just in error correction thresholds but in overall qubit properties. While error correction codes lower error rates, they demand much larger physical qubit counts as a tradeoff. An open question, therefore, is whether it will be easier to scale up these quantum computers to lower their error rates, or to pursue physical qubits with lower error rates. Either way, low error rates are the toll that must be paid to drive the FTQC highway and solve real-world problems with quantum computers.

Looking back at 2023, we jumped from experiments with 1-3 logical qubits up to 48. Logical qubits will form the “engines” of the quantum computer “vehicles” that you will be able to race along the FTQC highway, passing high-performance computers (HPC) on the side of the road as you solve some of the time-sensitive, data-intensive financial problems that they struggle with. In early 2024, the first two quantum roadmaps with logical qubits have already been published, and another is pending. Therefore, quantum advantage may be here sooner than expected.

However, quantum computing is not a plug-and-play technology; it takes time to upskill. In fact, many companies in the financial industry have been investing in quantum computing for years and have been developing an understanding of how to leverage it for relevant applications and integrate it into production pipelines. Companies that don’t start their journeys now may be late to the game. But it’s not too late yet; 2024 is the year to get behind the wheel and invest in some lessons so your competitors don’t beat you to the highway.

road to useful quantum computing

References

[1] W. C. Holton, "quantum computer," Britannica, 18 01 2024. [Online]. Available: https://www.britannica.com/technology/quantum-computer [Accessed 22 1 2024].

[2] D. L. Chelsea Whyte, "Timeline: A brief history of quantum computing from 1980 to 2100," New Scientist, 29 10 2019. [Online]. Available: https://www.newscientist.com/article/2221707-timeline-a-brief-history-of-quantum-computing-from-1980-to-2100/ [Accessed 22 1 2024].

[3] R. H. Stuewer, "Max Planck," Britannica, 22 12 2023. [Online]. Available: https://www.britannica.com/biography/Max-Planck [Accessed 22 1 2024].

[4] The Editors of Encyclopaedia Britannica, "digital computer," Britannica, 6 9 2022. [Online]. Available: https://www.britannica.com/technology/digital-computer [Accessed 22 1 2024].

[5] S. Aaronson, "Why Google’s Quantum Supremacy Milestone Matters," The New York Times, 30 10 2019. [Online]. Available: https://www.nytimes.com/2019/10/30/opinion/google-quantum-computer-sycamore.html [Accessed 22 1 2024].

[6] Y. Liu, Y. Chen, C. Guo, J. Song, X. Shi, L. Gan, W. Wu, W. Wu, H. Fu, X. Liu, D. Chen, Z. Zhao, G. Yang and J. Gao, "Verifying Quantum Advantage Experiments with Multiple Amplitude Tensor Network Contraction," Physical Review Letters, vol. 132, no. 3, p. 030601, 2024.

[7] QC Ware, "Q2B23 SV | The Future of Quantum Supremacy Experiments | Scott Aaronson," YouTube, 4 1 2024. [Online]. Available: https://www.youtube.com/watch?v=WWll3y_iBQU&t=369s [Accessed 22 1 2022].

[8] QC Ware, "Q2B 2022 SV | Ask Me Anything | Scott Aaronson | University of Texas at Austin," YouTube, 28 1 2023. [Online]. Available: https://www.youtube.com/watch?v=_SAeYQUQ27s&t=425s [Accessed 22 1 2024].

[9] QC Ware, "Q2B23 SV | The Future of Quantum Supremacy Experiments | Scott Aaronson," YouTube, 4 1 2024. [Online]. Available: https://www.youtube.com/watch?v=WWll3y_iBQU&t=471s [Accessed 22 1 2024].

[10] QC Ware, "Q2B23 SV | The Future of Quantum Supremacy Experiments | Scott Aaronson," YouTube, 4 1 2024. [Online]. Available: https://www.youtube.com/watch?v=WWll3y_iBQU&t=267s [Accessed 22 1 2024].

[11] E. Conover, "Google’s quantum computer reached an error-correcting milestone," ScienceNews, 22 2 2023. [Online]. Available: https://www.sciencenews.org/article/google-quantum-computer-sycamore-milestone [Accessed 22 1 2024].

[12] School of Engineering & Applied Science, "Doubling a Qubit's Life, Researchers Prove a Key Theory of Quantum Physics," Yale University, 22 3 2023. [Online]. Available: https://seas.yale.edu/news-events/news/doubling-qubit-s-life-researchers-prove-key-theory-quantum-physics [Accessed 22 1 2024].

[13] Xinhua News Agency, "Chinese scientists achieve breakthrough in quantum error correction," China.org.cn, 24 3 2023. [Online]. Available: http://www.china.org.cn/china/Off_the_Wire/2023-03/24/content_85190343.htm [Accessed 22 1 2024].

[14] H. Bombín, C. Dawson, N. Nickerson, M. Pant and J. Sullivan, "Increasing error tolerance in quantum computers with dynamic bias arrangement," arXiv, 28 3 2023. [Online]. Available: https://arxiv.org/abs/2303.16122v1 [Accessed 22 1 2024].

[15] K. Blackwood, "Physicists take step toward fault-tolerant quantum computing," Phys.org, 12 4 2023. [Online]. Available: https://phys.org/news/2023-04-physicists-fault-tolerant-quantum.html [Accessed 22 1 2024].

[16] "For the First Time Ever, Quantinuum’s New H2 Quantum Computer Has Created Non-Abelian Topological Quantum Matter and Braided its Anyons," Quantinuum, 9 5 2023. [Online]. Available: https://www.quantinuum.com/news/for-the-first-time-ever-quantinuums-new-h2-quantum-computer-has-created-non-abelian-topological-quantum-matter-and-braided-its-anyons [Accessed 22 1 2024].

[17] S. C. P. Williams, "Researchers develop 'noise-canceling' qubits to minimize errors in quantum computers," Phys.org, 25 5 2023. [Online]. Available: https://phys.org/news/2023-05-noise-canceling-qubits-minimize-errors-quantum.html [Accessed 22 1 2024].

[18] "QC Design Launches Plaquette: An All-Encompassing Quantum Error Correction and Fault-Tolerance Software Package," QC Design, 6 6 2023. [Online]. Available: https://www.qc.design/news/2023-06-07-plaquette-launch [Accessed 22 1 2024].

[19] R. Morrison, "Quantinuum builds fault-tolerant logical qubits," Tech Monitor, 13 7 2023. [Online]. Available: https://techmonitor.ai/hardware/quantum/quantinuum-builds-fault-tolerant-logical-qubits [Accessed 22 1 2024].

[20] S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall and T. J. Yoder, "High-threshold and low-overhead fault-tolerant quantum memory," arXiv, 15 8 2023. [Online]. Available: https://arxiv.org/abs/2308.07915 [Accessed 22 1 2024].

[21] Q. Xu, J. P. B. Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasic, M. D. Lukin, L. Jiang and H. Zhou, "Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays," SciRate, 21 8 2023. [Online]. Available: https://scirate.com/arxiv/2308.08648 [Accessed 22 1 2024].

[22] B. Barber, K. M. Barnes, T. Bialas, O. Buğdaycı, E. T. Campbell, N. I. Gillespie, K. Johar, R. Rajan, A. W. Richardson, L. Skoric, C. Topal, M. L. Turner and A. B. Ziad, "A real-time, scalable, fast and highly resource efficient decoder for a quantum computer," arXiv, 11 9 2023. [Online]. Available: https://arxiv.org/abs/2309.05558v1 [Accessed 22 1 2024].

[23] Y. Wang, S. Simsek, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, N. Hewitt, C. V. Horst, M. Matheny, T. Mengle, B. Neyenhuis and B. Criger, "Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code," SciRate, 19 9 2023. [Online]. Available: https://scirate.com/arxiv/2309.09893 [Accessed 22 1 2024].

[24] QuEra Computing Inc., "Harvard University, MIT and QuEra Demonstrate Historic 99.5% Two-Qubit Gate Fidelity on 60 Neutral Atom Qubits," 12 10 2023. [Online]. Available: https://www.quera.com/press-releases/harvard-university-mit-and-quera-demonstrate-historic-99-5-two-qubit-gate-fidelity-on-60-neutral-atom-qubits [Accessed 22 1 2024].

[25] M. Gross, "Two projects launched to connect error-corrected qubits," Eidgenössische Technische Hochschule Zürich, 1 11 2023. [Online]. Available: https://ethz.ch/en/news-and-events/eth-news/news/2023/11/two-projects-launched-to-connect-error-corrected-qubits.html [Accessed 22 1 2024].

[26] Y. Ye, et al., "Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor," Physical Review Letters, vol. 131, no. 21, p. 210603, 2023.

[27] J. Russell, "re:Invent 2023: AWS Talks a Little Quantum, Showcases Error Correction Progress," HPC wire, 28 11 2023. [Online]. Available: https://www.hpcwire.com/2023/11/28/reinvent-2023-aws-talks-a-little-quantum-showcases-error-correction-progress/ [Accessed 22 1 2024].

[28] QuEra Computing Inc., "Harvard, QuEra, MIT, and the NIST/University of Maryland Usher in New Era of Quantum Computing by Performing Complex, Error-Corrected Quantum Algorithms on 48 Logical Qubits," 6 12 2023. [Online]. Available: https://www.quera.com/press-releases/harvard-quera-mit-and-the-nist-university-of-maryland-usher-in-new-era-of-quantum-computing-by-performing-complex-error-corrected-quantum-algorithms-on-48-logical-qubits [Accessed 22 1 2024].

[29] HKA Marketing Communications, "Alice & Bob tapes out quantum chip to perform error correction and to demonstrate a logical qubit prototype," EIN Presswire, 19 12 2023. [Online]. Available: https://www.einnews.com/pr_news/675967097/alice-bob-tapes-out-quantum-chip-to-perform-error-correction-and-to-demonstrate-a-logical-qubit-prototype [Accessed 22 1 2024].

[30] QuEra Computing Inc., "QuEra Computing Releases a Groundbreaking Roadmap for Advanced Error-Corrected Quantum Computers, Pioneering the Next Frontier in Quantum Innovation," 9 1 2024. [Online]. Available: https://www.quera.com/press-releases/quera-computing-releases-a-groundbreaking-roadmap-for-advanced-error-corrected-quantum-computers-pioneering-the-next-frontier-in-quantum-innovation [Accessed 22 1 2024].

[31] Alice & Bob, "[Teaser] What if quantum could happen much sooner than expected?," LinkedIn, 17 1 2024. [Online]. Available: https://www.linkedin.com/posts/alice-bob_teaser-what-if-quantum-could-happen-much-activity-7153023153890344960-98q_/?utm_source=share&utm_medium=member_desktop [Accessed 22 1 2024].

[32] "Infleqtion Unveils 5-year Quantum Computing Roadmap, Advancing Plans to Commercialize Quantum at Scale," ColdQuanta, Inc., DBA Infleqtion, 8 2 2024. [Online]. Available: https://www.infleqtion.com/news/infleqtion-unveils-5-year-quantum-computing-roadmap-advancing-plans-to-commercialize-quantum-at-scale [Accessed 12 2 2024].

[33] R. Wu, "Optimize hybrid quantum-classical algorithms directly with Fire Opal," Q-CTRL, 4 4 2023. [Online]. Available: https://q-ctrl.com/blog/optimize-hybrid-quantum-classical-algorithms-directly-with-fire-opal [Accessed 22 1 2024].

[34] C. Campbell, et al., "Superstaq: Deep Optimization of Quantum Programs," arXiv, 10 9 2023. [Online]. Available: https://arxiv.org/abs/2309.05157 [Accessed 22 1 2024].

[35] H. Liao, D. S. Wang, I. Sitdikov, C. Salcedo, A. Seif and Z. K. Minev, "Machine Learning for Practical Quantum Error Mitigation," arXiv, 29 9 2023. [Online]. Available: https://arxiv.org/abs/2309.17368v1 [Accessed 22 1 2024].

[36] HKA Marketing Communications, "Q-CTRL Integrates Its Error Suppression Technology into IBM Quantum services," WIVB-TV, 28 11 2023. [Online]. Available: https://www.wivb.com/business/press-releases/ein-presswire/671420681/q-ctrl-integrates-its-error-suppression-technology-into-ibm-quantum-services/ [Accessed 22 1 2024].